Inelastic Collision Calculator
Enter masses and velocities of two objects to compute the final velocity, momentum and kinetic energy lost in a perfectly inelastic collision.
Input Data
Results
At a glance:A perfectly inelastic collision is one where the two bodies stick together after impact. Momentum is conserved: m1·v1 + m2·v2 = (m1+m2)·v_f, so v_f = (m1·v1 + m2·v2)/(m1+m2). Kinetic energy is NOT conserved — some converts to heat, sound and deformation. The lost fraction is 1 − KE_after/KE_before. Maximum KE loss for a given initial momentum occurs in a perfectly inelastic collision (compared with elastic, where KE is conserved). This tool reports v_f, momentum before/after (which match, verifying conservation), KE before/after and the percent lost.
Formula
Momentum conserved: m1v1 + m2v2 = (m1+m2)v_f
v_f = (m1v1 + m2v2)/(m1+m2)
KE lost % = (1 − KE_after/KE_before)·100
$$v' = \dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$$$$\Delta KE = \dfrac{1}{2}\dfrac{m_1 m_2}{m_1 + m_2}(v_1 - v_2)^2$$How to Use
- Enter masses m1, m2 and velocities v1, v2.
- The calculator returns v_f, momenta, kinetic energies and % lost.
Case Studies
Clay balls collide
m1 = 2 kg v1 = 3 m/s, m2 = 1 kg v2 = 0.
v_f = 6/3 = 2 m/s.
KE_before = 9 J, KE_after = 6 J, 33% lost.
FAQ
Why is momentum conserved but not kinetic energy?
No external force acts during the short collision, so total momentum is conserved. But the impact is irreversible (deformation, heat), so mechanical KE decreases — energy is transformed, not destroyed.
What if they don't stick?
That is a partially inelastic (or elastic) collision. 'Perfectly inelastic' specifically means they coalesce; this tool handles that case.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.